The mean and standard deviation for the heights of adult men are about 70 inches and 3 inches, respectively; for adult women, they are about 65 inches and 2.5 inches, respectively. Heights within each sex are bell-shaped. Suppose random samples of nine men's and nine women's heights are measured and the difference in the sample means is found (men - women).
a. What is the mean of the sampling distribution of x‾1 - x‾2 in this situation?
b. What is the standard deviation of the sampling distri bution?
c. Draw a picture of the sampling distribution of x‾1 - x‾2, similar to given Figure.
d. Is it possible that the mean height for the sample of women will be greater than the mean height for the sample of men? Explain.
